This invention relates in general to piezoelectric crystal resonators for use either in an electric oscillator or in an electric filter; and more particularly, it relates to AT-cut or R.sub.1 -cut piezoelectric crystal resonators of extremely small overall dimensions.
As is well known, the AT-cut crystal resonator is most efficient and superior among known various type of resonators. With recent advancement of technology, it has been endevored towards miniaturized At-cut crystal resonators. In this respect, James J. Royer has made profound experiments and studies (refer to his thesis entitled "A New DT Quartz Resonator" and published in "IEEE-Transactions on Sonics and Ultrasonics", Vol. SU - 17, No. 1, January 1970).
Royer concludes that when the AT-cut resonator is reduced gradually in its Z'-axis dimension according to his definition, it operates at last substantially as a DT-cut one. He proposes the length to dimension of width (Y' according to his definition) must be larger than 20, and the plano-length 1.sub.1 between the bevels must be 30-60% of the length of the resonator. Even with satisfaction of such dimensional requirements, however, Q amounts only to 50,000-100,000. In addition, fired silver counter weights as mass loadings must be provided at the both ends of the resonator plate, in order to supress anharmonics, thereby reducing unwanted spurious oscillations. The most interesting subject of the Royer's resonator is its frequency-temperature curve in the form of DT-characteristic one which is demonstrated on page 22 of his thesis. This curve is similar to the DT-characteristic curve shown on page 29 of "Quartz Crystals for Electrical Circuits", second edition, authored by R. A. Heising and published by D. Van Nostrand Company, Inc., New York. It is thus seen that the frequency-temperature curve of Royer's resonator is far from the AT-curve in the form of cubic one, as demonstrated on the same page 29 of the Heising's publication. My invention aims at the realization of an ideal AT-curve as mentioned above, of highly miniaturized AT-cut crystal resonator without accompanying unwanted spurious reponses.